This section
explored the many different problems you may be faced with when having to
find an average.

It also shows
a number of examples of COMPARING distributions.

AVERAGES from Tables

Below is an
example of a table of CONTINUOUS data

To estimate the mean:

·We to find the mid-points of each of the classes which I will write in red

·We also need to find the total
frequency

Height

Frequency

(2.5)

3

(7.5)

2

(15)

6

(30)

1

TOTAL

12

To estimate the MEDIAN without drawing a cumulative
frequency graph

To find
which value is the MEDIAN we use the formula

In this
case, n=12

The 6th
and the 7th value are both in the class: . So our median class
is

AVERAGES from STEM and LEAF diagrams

This
table shows pocket money of boys in a
class

1

1
2 4 6 7

KEY

1

1

=
£11

2

1
2 2 2 5 5 7

3

3
4 5 6

4

1
9

5

2
2 3

We already know that the girls have got a mean of £23, a
median of £26 and a range of £30.

QUESTION: Compare the amount which boys and girls
receive in pocket money.

Boy’s
mean: we
need to add up each value in the stem and leaf diagram and divide by the
number of numbers there are

Boy’s
median: we
know that n=21

If we count along to
find the 11th value we find it is £25

Boy’s
range:

Comparison:

1)The
boys’ range is £42 which is £12 more than the girl’s range. This means the
amount which boy’s received is more spread out/less consistent.

2)The
boy’s mean of £29.50 is £6.50 more than the girl’s mean. However, the boy’s
median of £25 is £1 less. On balance, however, you would suggest that the higher
mean indicated that boy’s, on average, receive MORE pocket money

MEDIAN’s and QUARTILES WITHOUT a cumulative
frequency graph

Assuming the data is given in ascending
order (if not, you need to re-arrange it first)